GOALSThe goals for this Unit are:
CCGPS - Math Standards HS Georgia Standards of Excellence Primary CCGPS Standards attempted to address in this unit: Circles G.C Understand and apply theorems about circles MCC9‐12.G.C.1 Prove that all circles are similar. MCC9‐12.G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. MCC9‐12.G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. MCC9‐12.G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle. Find arc lengths and areas of sectors of circles MCC9‐12.G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Georgia Standards for Mathematical Practice
Other Secondary CCGPS Standards addressed in this unit: Congruence G.CO Experiment with transformations in the plane MCC9‐12.G.CO.1 Know precise definitions of angle, CIRCLE, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MCC9‐12.G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). MCC9‐12.G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. MCC9‐12.G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions MCC9‐12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Similarity, Right Triangles, and Trigonometry G.SRT Understand similarity in terms of similarity transformations MCC9‐12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Students will benefit from Group Learning as they explore the technology together in small groups. They will also benefit from Integrated Learning by combining Technology, Circles, Transformations, Congruence and Similarity. |